Shear Stresses and Deflections in Beams

The vertical shear stress in an elastic beam is given by, 

The above solution is only valid for beams whose cross-sectional dimensions are small compared to the length. That is if b . JL is approximately 10 or larger. For beams that do not meet this condition, deflections 

However, as long as the material is linear, the correspondence principle can be used to obtain viscoelastic solutions from the appropriate elastic solution. It is well to note that such shear corrections are more important for polymeric materials than for metals as moduli are smaller and deformations are correspondingly larger. Therefore, shear corrections are typically more important. 

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